Gyroscopic Steering Tool Using Only a Two-Axis Rate Gyroscope and Deriving the Missing Third Axis

ABSTRACT

A two-axis gyroscope used on a bottom hole assembly can be used for determining a rate of rotation about the rotational axis of a BHA. The method takes advantage of possible misalignment of at least one axis of the two axis gyroscope from orthogonality with respect to the rotational axis of the BHA, resulting in the misaligned gyro being sensitive to BHA rotation.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a divisional application of U.S. application Ser.No. 10/911,921 filed on Aug. 5, 2004, which claims priority from U.S.Provisional Patent Application Ser. No. 60/493,300 filed on Aug. 7,2003.

FIELD OF THE INVENTION

This invention relates generally to bottom hole assemblies for drillingoilfield wellbores and more particularly to the use of gyroscopic andother sensors to determine wellbore and drilling tool direction duringthe drilling of the wellbores and to the correction of data from suchsensors.

BACKGROUND OF THE INVENTION

To obtain hydrocarbons such as oil and gas, wellbores (also referred toas the boreholes) are drilled by rotating a drill bit attached at theend of a drilling assembly generally referred to as the “bottom holeassembly” (BHA) or the “drilling assembly.” A large portion of thecurrent drilling activity involves drilling highly deviated andsubstantially horizontal wellbores to increase the hydrocarbonproduction and/or to withdraw additional hydrocarbons from the earth'sformations. The wellbore path of such wells is carefully planned priorto drilling such wellbores utilizing seismic maps of the earth'ssubsurface and well data from previously drilled wellbores in theassociated oil fields. Due to the very high cost of drilling suchwellbores and the need to precisely place such wellbores in thereservoirs, it is essential to frequently determine the position anddirection of the drilling assembly and thus the drill bit duringdrilling of the wellbores. Such information is utilized, among otherthings, to monitor and adjust the drilling direction of the wellbores.It should be noted that the terms “wellbore” and “borehole” are usedinterchangeably in the present document.

In the commonly used drilling assemblies, the directional packagecommonly includes a set of accelerometers and a set of magnetometers,which respectively measure the earth's gravity and magnetic fields. Thedrilling assembly is held stationary during the taking of themeasurements from the accelerometers and the magnetometers. The toolfaceand the inclination angle are determined from the accelerometermeasurements. The azimuth is then determined from the magnetometermeasurements in conjunction with the tool face and inclination angle. Asused herein, the term “toolface” means the orientation angle of the benthousing or sub in the borehole with respect to a reference such as highside of the borehole which indicates the direction in which the boreholewill be curving. The inclination angle is the angle between the boreholeaxis and the vertical (direction of the gravity field). The azimuth isthe angle between the horizontal projection of the borehole axis and areference direction such as magnetic north or absolute north.

The earth's magnetic field varies from day to day, which causescorresponding changes in the magnetic azimuth. The varying magneticazimuth compromises the accuracy of the position measurements whenmagnetometers are used. Additionally, it is not feasible to measure theearth's magnetic field in the presence of ferrous or ferromagneticmaterials, such as casing and drill pipe. Gyroscopes measure the rate ofthe earth's rotation, which does not change with time nor are thegyroscopes adversely affected by the presence of ferrous materials.Thus, in the presence of ferrous materials the gyroscopic measurementscan provide more accurate azimuth measurements than the magnetometermeasurements.

U.S. Pat. No. 5,432,699 of Hache et al. discloses a method and apparatusmeasuring motion signals of gyroscopes in downhole instruments used todetermine the heading of a borehole. Accelerometer and magnetometer dataalong three orthogonal axes of a measurement sub are used to obtain unitgravitational and magnetic vectors. The gyroscope measurements are usedto correct the magnetic and gravity measurements made by themagnetometer and the accelerometer respectively. The calculationsperformed in the correction process by this, and other prior artoptimization schemes based upon least squares methods, are valid whenthe measurements are corrupted by random additive noise. As would beknown to those versed in the art, in the presence of systematicmeasurement errors, such least-squares optimization methods areunreliable.

Commercially available gyroscopes contain systematic errors or biasesthat can severely deteriorate accuracy of a gyroscope's measurements andthus the azimuth. Gyroscopes have been utilized in wireline surveyapplications but have not found commercial acceptance in themeasurement-while-drilling (MWD) tools used in bottomhole assemblies.

In wireline applications, the survey tool is conveyed into the wellboreafter the wellbore has been drilled, in contrast to the MWD toolswherein the measurements are made during the drilling of the wellbores.Wireline methods are not practical in determining the drilling assemblyposition and direction during the drilling of the wellbores. In wirelineapplications, the gyroscopes are used either in a continuous mode or atdiscrete survey intervals. Wireline survey methods often make itunnecessary to employ techniques to compensate for the present-value ofthe gyroscope biases. In wireline applications, the gyroscope can bepowered-up at the surface and allowed to stabilize (thermally anddynamically) for a relatively long time period. Typically a warm-upperiod of ten (10) minutes or more is taken. The power to the gyroscopeis continuously applied from the beginning at the surface, through theactual wellbore survey and through the final check of the survey tool atthe surface at the end of the survey. Therefore, reference alignmentscan be made at the surface prior to commencing the wellbore survey toadjust the drift in a gimbaled gyroscope or verify the alignmentaccuracy of a north-seeking gyroscope. The initial independent referencecan then be used at the end of the wireline survey. Any bias in thegyroscope in a wireline tool can be measured at the surface by takingthe difference in the alignments at the beginning and the end of thesurvey runs. Furthermore, the wireline tool carrying the north-seekinggyroscope can easily be rotated at the surface to several differenttoolface (roll angle) positions to determine the bias present on eitherof the transverse gyroscopes (i.e., along the x and y axis of the tool)when the tool is at the surface. This bias can be used to verify theaccuracy or to correct the gyroscope measurements.

In the MWD environment, the above-noted advantages of the wirelinesystems are not present. The MWD surveys are usually taken during drillpipe connection times during the drilling of the wellbore, whichintervals are relatively short—generally one to four minutes. Power inthe MWD tools is generated downhole and/or provided by batteries. Toconserve the power, it is desirable to switch off the gyroscopes whennot in use because the gyroscopes consume considerable power. For MWDtools utilizing turbine-alternator, the power is generated by flow ofthe drilling fluid (“mud”) which is interrupted at each pipe connection.Even if the power could be applied continuously, the difference in thebias measured at the surface prior to the drilling and post drilling isnot considered an accurate measure due to the very long time betweendrilling assembly trips, which are typically between 20 and 200 hours.

Earlier 2-axis (X-Y) gyro tools could be used for North-Seekinggyrocompass operations when the tool is vertical up to about 60 degreesinclination. This is a static operation, which is done during pipeconnections while there is no motion of the drillstring. Gyroscopicsteering of oilfield drilling assemblies is typically accomplished bythe addition of a 3rd (Z-axis) gyro which is oriented to measure therotation of the toolface along the long axis of the drillstring. Anexample of such a device is disclosed in U.S. Pat. No. 6,347,282 andU.S. Pat. No. 6,529,834 to Estes et al, having the same assignee and thecontents of which are incorporated herein by reference. With slim (1¾″OD) tools, there is very little room to accommodate a 3rd gyro axismounted crosswise to the X and Y axes, which are often realized in asingle, 2-axis rate gyroscope.

Prior art devices have added a smaller, less accurate rate gyro in theZ-axis to allow direct measurements of the angular rotation rate in theZ-axis (toolface). By integrating this Z-axis rate, these tools cantrack changes in the toolface angular orientation as the drilling motorand deviation device (bent sub) are sliding down the borehole. However,the resultant accuracy leaves a lot to be desired.

Attempts by the applicant to track toolface using only the Rate-X andRate-Y measurements have been made using a modification of the originalgyrocompassing technique. On the theory that there may be some timeperiods when the BHA is still enough to allow using the conventionalNorth-seeking operation to work, a “Fast Intermittent Gyrocompassing”technique was tested. Laboratory tests showed that the extremedifference between earth rate (15 deg/hr) and toolface changes duringtypical drilling (˜45 deg/sec or ˜162,000 deg/hr) caused detectionproblems. There is no guarantee the platform will ever be stable, and noindependent indicator of a sufficiently stable condition. Even minusculedrillstring relaxation after a drilling period is likely to introducelarge rate errors in trying to measure the earth's rotation.

It is desirable to be able to track toolface changes during steering,using only an (X-Y) 2-axis rate gyro sensor. The present inventionsatisfies this need.

SUMMARY OF THE INVENTION

The present invention is a method of using a two-axis gyroscope on ahousing for determining a rate of said housing about a third axis, whenthe two axes of the two-axis gyroscope are substantially orthogonal toeach other and to the third (the z) axis, but at least one of these twogyroscope axes has a small deviation from orthogonality relative to thethird axis. Under these conditions, the misaligned gyro has asensitivity to rotation about the third axis. This makes it possible todetermine the toolface angle of a drilling assembly with only a two-axisgyro. Using calibration procedures, the major temperature-dependenterrors within the gyros are removed. Using prior art indexingprocedures, residual bias values for each of the two axes are determinedand removed. By rotating the assembly at a known rate about the thirdaxis, the cross-sensitivity can be determined, in the laboratory ordownhole, and then subsequently used for determining rotation about thez-axis of the drilling assembly.

The gyro may be conveyed downhole on a drilling tubular or on awireline. When used in conjunction with a drilling tubular, the methodof the present invention is particularly useful in directional drillingoperations.

BRIEF DESCRIPTION OF THE DRAWINGS

For detailed understanding of the present invention, references shouldbe made to the following detailed description of the preferredembodiment, taken in conjunction with the accompanying drawings, inwhich like elements have been given like numerals, wherein:

FIG. 1 shows a schematic diagram of a drilling system that employs theapparatus of the current invention in a measurement-while-drillingembodiment;

FIG. 2 shows a schematic diagram of a portion of the bottomhole assemblywith a set of gyroscopes and a corresponding set of accelerometersaccording to a preferred embodiment of the present invention;

FIG. 3 is a flow chart illustrating a method for determining a deviationfrom orthogonality between a gyro axis and an axis of rotation intendedto be orthogonal to the gyro axis;

FIG. 4 illustrates the method of the present invention for use incontrolling drilling operations;

FIGS. 5A-5C illustrate the survey mode of FIG. 4;

FIG. 6 illustrates a method of correcting downhole measurements usinglaboratory derived calibrations;

FIG. 7 illustrates the steering mode of FIG. 4;

FIG. 8 illustrates the effect of temperature drift on gyroscopemeasurements;

FIG. 9 shows the results of a sinusoidal curve fitting to measurementsaffected by temperature drift;

FIG. 10 shows residuals from FIG. 9 as a function of nominaltemperature; and

FIG. 11 shows bias determination correcting for the effects oftemperature drift.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a schematic diagram of a drilling system 10 having a bottomhole assembly (BHA) or drilling assembly 90 that includes gyroscope(s)according to the present invention. The BHA 90 is conveyed in a borehole26. The drilling system 10 includes a conventional derrick 11 erected ona floor 12 which supports a rotary table 14 that is rotated by a primemover such as an electric motor (not shown) at a desired rotationalspeed. The drill string 20 includes a tubing (drill pipe orcoiled-tubing) 22 extending downward from the surface into the borehole26. A drill bit 50, attached to the drill string 20 end, disintegratesthe geological formations when it is rotated to drill the borehole 26.The drill string 20 is coupled to a drawworks 30 via a kelly joint 21,swivel 28 and line 29 through a pulley (not shown). Drawworks 30 isoperated to control the weight on bit (“WOB”), which is an importantparameter that affects the rate of penetration (“ROP”). A tubinginjector 14 a and a reel (not shown) are used as instead of the rotarytable 14 to inject the BHA into the wellbore when a coiled-tubing isused as the conveying member 22. The operations of the drawworks 30 andthe tubing injector 14 a are known in the art and are thus not describedin detail herein.

During drilling, a suitable drilling fluid 31 from a mud pit (source) 32is circulated under pressure through the drill string 20 by a mud pump34. The drilling fluid passes from the mud pump 34 into the drill string20 via a desurger 36 and the fluid line 38. The drilling fluid 31discharges at the borehole bottom 51 through openings in the drill bit50. The drilling fluid 31 circulates uphole through the annular space 27between the drill string 20 and the borehole 26 and returns to the mudpit 32 via a return line 35 and drill cutting screen 85 that removes thedrill cuttings 86 from the returning drilling fluid 31 b. A sensor S₁ inline 38 provides information about the fluid flow rate. A surface torquesensor S₂ and a sensor S₃ associated with the drill string 20respectively provide information about the torque and the rotationalspeed of the drill string 20. Tubing injection speed is determined fromthe sensor S₅, while the sensor S₆ provides the hook load of the drillstring 20.

In some applications the drill bit 50 is rotated by only rotating thedrill pipe 22. However, in many other applications, a downhole motor 55(mud motor) is disposed in the drilling assembly 90 to rotate the drillbit 50 and the drill pipe 22 is rotated usually to supplement therotational power, if required, and to effect changes in the drillingdirection. In either case, the ROP for a given BHA largely depends onthe WOB or the thrust force on the drill bit 50 and its rotationalspeed.

The mud motor 55 is coupled to the drill bit 50 via a drive disposed ina bearing assembly 57. The mud motor 55 rotates the drill bit 50 whenthe drilling fluid 31 passes through the mud motor 55 under pressure.The bearing assembly 57 supports the radial and axial forces of thedrill bit 50, the downthrust of the mud motor 55 and the reactive upwardloading from the applied weight on bit. A lower stabilizer 58 a coupledto the bearing assembly 57 acts as a centralizer for the lowermostportion of the drill string 20.

A surface control unit or processor 40 receives signals from thedownhole sensors and devices via a sensor 43 placed in the fluid line 38and signals from sensors S₁-S₆ and other sensors used in the system 10and processes such signals according to programmed instructions providedto the surface control unit 40. The surface control unit 40 displaysdesired drilling parameters and other information on a display/monitor42 that is utilized by an operator to control the drilling operations.The surface control unit 40 contains a computer, memory for storingdata, recorder for recording data and other peripherals. The surfacecontrol unit 40 also includes a simulation model and processes dataaccording to programmed instructions. The control unit 40 is preferablyadapted to activate alarms 44 when certain unsafe or undesirableoperating conditions occur.

The BHA may also contain formation evaluation sensors or devices fordetermining resistivity, density and porosity of the formationssurrounding the BHA. A gamma ray device for measuring the natural gammaray intensity and other nuclear and non-nuclear devices used asmeasurement-while-drilling devices are suitably included in the BHA 90.As an example, FIG. 1 shows a resistivity measuring device 64. Itprovides signals from which resistivity of the formation near or infront of the drill bit 50 is determined. The resistivity device 64 hastransmitting antennae 66 a and 66 b spaced from the receiving antennae68 a and 68 b. In operation, the transmitted electromagnetic waves areperturbed as they propagate through the formation surrounding theresistivity device 64. The receiving antennae 68 a and 68 b detect theperturbed waves. Formation resistivity is derived from the phase andamplitude of the detected signals. The detected signals are processed bya downhole computer 70 to determine the resistivity and dielectricvalues.

An inclinometer 74 and a gamma ray device 76 are suitably placed alongthe resistivity measuring device 64 for respectively determining theinclination of the portion of the drill string near the drill bit 50 andthe formation gamma ray intensity. Any suitable inclinometer and gammaray device, however, may be utilized for the purposes of this invention.In addition, position sensors, such as accelerometers, magnetometers ora gyroscopic devices may be disposed in the BHA to determine the drillstring azimuth, true coordinates and direction in the wellbore 26. Suchdevices are known in the art and are not described in detail herein.

In the above-described configuration, the mud motor 55 transfers powerto the drill bit 50 via one or more hollow shafts that run through theresistivity measuring device 64. The hollow shaft enables the drillingfluid to pass from the mud motor 55 to the drill bit 50. In an alternateembodiment of the drill string 20, the mud motor 55 may be coupled belowresistivity measuring device 64 or at any other suitable place. Theabove described resistivity device, gamma ray device and theinclinometer are preferably placed in a common housing that may becoupled to the motor. The devices for measuring formation porosity,permeability and density (collectively designated by numeral 78) arepreferably placed above the mud motor 55. Such devices are known in theart and are thus not described in any detail.

As noted earlier, a large portion of the current drilling systems,especially for drilling highly deviated and horizontal wellbores,utilize coiled-tubing for conveying the drilling assembly downhole. Insuch application a thruster 71 is deployed in the drill string 90 toprovide the required force on the drill bit. For the purpose of thisinvention, the term weight on bit is used to denote the force on the bitapplied to the drill bit during the drilling operation, whether appliedby adjusting the weight of the drill string or by thrusters. Also, whencoiled-tubing is utilized the tubing is not rotated by a rotary table,instead it is injected into the wellbore by a suitable injector 14 awhile the downhole motor 55 rotates the drill bit 50.

A number of sensors are also placed in the various individual devices inthe drilling assembly. For example, a variety of sensors are placed inthe mud motor power section, bearing assembly, drill shaft, tubing anddrill bit to determine the condition of such elements during drillingand to determine the borehole parameters. The preferred manner ofdeploying certain sensors in drill string 90 will now be described. Theactual BHA utilized for a particular application may contain some or allof the above described sensors. For the purpose of this invention anysuch BHA could contain one or more gyroscopes and a set ofaccelerometers (collectively represented herein by numeral 88) at asuitable location in the BHA 90. A preferred configuration of suchsensors is shown in FIG. 2.

FIG. 2 is a schematic diagram showing a sensor section 200 containing agyroscope 202 and a set of three accelerometers 204 x, 204 y and 204 zdisposed at a suitable location in the bottomhole assembly (90 inFIG. 1) according to one preferred embodiment of the present invention.The gyroscopes 202 may be a single axis gyroscope or a two-axisgyroscope. In vertical and low inclination wellbores, an x-axis and ay-axis gyroscope are deemed sufficient for determining the azimuth andtoolface with respect to the true north. The configuration shown in FIG.2 utilizes a single two-axis (x-axis and y-axis) gyroscope that providesoutputs corresponding to the earth's rate of rotation in the two axis(x-axis and y-axis) perpendicular to the borehole axis or the bottomholeassembly longitudinal axis, referred to herein as the z-axis. The sensor202 thus measures the earth's rotation component in the x-axis andy-axis. The accelerometers 204 x, 204 y and 204 z measure the earth'sgravity components respectively along the x, y, and z axes of thebottomhole assembly 90.

The gyroscope 202 and accelerometers 204 x-204 z are disposed in arotating chassis 210 that rotates about the radial bearings 212 a-212 bin a fixed or non-rotating housing 214. An indexing drive motor 216coupled to the rotating chassis 210 via a shaft 218 can rotate thechassis 210 in the bottomhole assembly 90 about the z-axis, thusrotating the gyroscopes 202 from one mechanical position to anotherposition by any desired rotational angle. A stepper motor is preferredas the indexing drive motor 216 because stepper motors are precisiondevices and provide positive feedback about the amount of rotation. Anyother mechanism, whether electrically-operated, hydraulically-operatedor by any other desired manner, may be utilized to rotate the gyroscopeswithin the bottomhole assembly 90. The gyroscope 202 may be rotated froman initial arbitrary position to a mechanical stop (not shown) in thetool or between two mechanical stops or from an initial peak measurementto a second position as described later. The rotational anglecorresponding to a particular axis is selectable.

Although FIG. 2 shows a single two axis gyroscope, a separate gyroscopemay be utilized for each axis. A wiring harness 226 provides power tothe gyroscope 202 and accelerometers 204 x, 204 y, 204 z. The wiringharness 226 transmits signals from the gyroscope and accelerometers tothe processor in the bottomhole assembly 90. Similarly, a suitablewiring harness 220 provides power and signal linkage to the steppermotor 216 and additional downhole equipment. A spring loaded torquelimiter 240 may be used to prevent inertial loading caused bydrillstring rotation from damaging the gearbox of the stepper motor 216.Alternatively, a preset torque slip clutch may be used.

The present invention is based on the fact that in actual implementationof a two-axis gyroscope (designated herein as the x- and y-axes), theaxes are not exactly orthogonal to each other. Recognizing the fact thatthe x- and y-axes of the rate gyro are not precisely orthogonal to thephysical z-axis, then it is clear that there is some responsiveness ofthe x- and y-rate measurements to a rotation in the z-axis. This may bedenoted by the equation: $\begin{matrix}{R_{x} = {\frac{S_{x}}{F_{x}} - B_{x} - B_{xg} - {M_{x}R_{z}}}} & (1)\end{matrix}$where R_(x) is the x-axis rate, S_(x) is the output of the x-axis gyro,F_(x) is a calibration scale factor for the x-axis gyro, B_(x) is thebias in the x-axis gyro, B_(xg) is a bias term that is gravity related,i.e., it depends on the inclination of the tool, M_(x) is a misalignmentterm relating the z-axis rotation rate R_(z) to the x-axis gyro measuredrate. If the x-axis is exactly orthogonal to the z-axis, thismisalignment term is zero. This is the assumption that is made in priorart devices. A similar expression may be used for the y-axis rate R_(y).$\begin{matrix}{R_{y} = {\frac{S_{y}}{F_{y}} - B_{y} - B_{yg} - {M_{y}R_{z}}}} & (2)\end{matrix}$

We digress briefly to distinguish the subject matter of the presentinvention from Algrain, “Determination of 3-D angular rates usingtwo-axis measurements,” SPIE Vol. 2468, pp 252-260. While the title issuperficially similar to the subject of the present invention, Algrainaddresses the problem of using perfectly aligned 2-axis gyros on anobject in space (free of the gravity field of the earth) to determine arotation rate about the third axis. The formulation of the problem iscompletely different from the present situation wherein imperfectlyaligned 2-axis gyro measurements made in the earth's gravity field areused to estimate a rotation rate about the third axis.

The calibration scale factors F_(x) and F_(y) are determined using priorart methods—these calibration factors simply relate the output of the x-and y-gyros (which are typically in millivolts) to the x- and y-axisrotation rates. A simple way to determine the misalignment terms in alaboratory setting is first described next with reference to FIG. 3.

Initially, the tool is oriented with its (z) axis inclined vertically sothat the gravity terms B_(xg), B_(yg) are zero. This is not alimitation, as a calibration could be carried out with otherorientations of the tool as well but would require the use ofaccelerometer measurements to zero out these terms and complete thecalibration. Hence to simplify the discussion, it is assumed that thegravity terms are zero. The scale factors F_(x) and F_(y) are knownquantities. Using prior art methods such as that described in either ofthe Estes patents, bias values are estimated for the x- and y-gyros 103.At least two methods are described in the Estes patents. In one of them,gyro readings are taken with one toolface orientation of the tool, thehousing is rotated by 180°, and a second gyro reading is taken. In theabsence of a bias, readings spaced 180° apart should sum to zero. Anydifference from zero of this sum is a measure of the bias in the gyromeasurement. In a second method described in the Estes patents, thesensor housing is rotated (preferably using a stepper motor) and byfitting a sinusoid to the readings, bias can be determined.

In a laboratory setting, the misalignment term can be estimated by nowrotating the housing at a known rate 105. If the bias corrected x- andy-gyros give a value different from the expected values due to thepresence of earth rate, then the misalignment terms are directlyobtained as the ratio of the bias corrected measurements and the knownrate of rotation about the z-axis 107.

Once the misalignment term has been determined, the outputs of the x-and y-gyros can be used to determine a z-axis rotation rate when thereis such actual rotation. This is because the bias terms are now knownfor the x- and y-gyros, and the gravity term is known from accelerometerand gyro measurements.

The same principle can be used in actual wellbore applications. Someimportant steps for this are discussed below. However, before discussinghow such a method may be implemented in surveying and steeringoperations, a few comments about the z-axis rotation are in order.

The earth's rotation rate is approximately 15.1 deg/hr (approximately264 milliradians per hour). The changes in borehole inclination and inborehole azimuth are typically of the same or lesser order of magnitude.In contrast, for a drillstring rotation speed of even 60 rpm, the changein tool face angle is 1,296,000 deg/hr, which is five orders ofmagnitude greater than the earth's rotation rate. Hence even if a z-axisgyro were mounted on the surveying tool, it would be difficult for sucha z-axis gyro to maintain accuracy over such a large dynamic range. Atypical misalignment for gyros is of the order of 10 milliradians. Theeffect of such a misalignment gives a resultant signal on the x- andy-gyros that is comparable in magnitude to measurements normally made bygyros on an MWD tool. Hence the present invention actually takesadvantage of the misalignment to give reasonably accurate measurementsof toolface angle.

Turning now to FIG. 4, the three major modes of operation areidentified. The first is the surface calibration 401 whereinmisalignment of the gyros is determined using methods discussed abovewith reference to FIG. 3. This step is not essential, but as describedbelow, is helpful in what follows later in the wellbore. In the “surveymode” 403, measurements are carried out at a substantially fixedposition of the gyro assembly. The survey mode is followed by a“steering mode” 405 wherein the drillbit is actually making hole withthe drillbit turning and powered by a mud motor. The survey mode iscommonly used when additional sections of drillpipe are being added.

Turning now to FIG. 5B, some of the steps that could be carried out inthe survey mode are discussed. It is to be noted that while these aredescribed with reference to a flow chart, some of the “steps” identifiedneed not necessarily be carried out in the sequence described. The onlyimplication of a “sequence” of steps is if a particular operationrequires the output of another operation. In all other cases, some ofthe operations could be carried out in parallel or even in a differentorder than that shown here. The “flow chart” is shown mainly as a matterof convenience to identify the different operations that could becarried out. A general guide to the operations is also given in alisting in the Appendix below. A static survey is initiated after aprogrammed delay 501. The limits of mechanical travel of the housingcarrying the sensors are determined 503 and a midpoint may be defined asthe “zero” point 505. Measurements are made with all the sensors on thesurvey assembly (x- and y-gyros, x-, y- and z-accelerometers andmagnetometers if provided) at the “zero” position 507. The indexingprocess is carried out as described in the Estes patents. In theindexing, measurements are made at the “zero” reading, and at ±20°, ±40°and ±60°, with a measurement taken at the “zero” mark each time 507. Itis not essential that these exact values be used, or even that such anumber of measurements be made. Next, a polynomial fit is carried out tothe measurements made by each of the plurality of sensors at the “zero”mark 511. In an alternate embodiment of the invention, nine readings aretaken 40° apart without repeating the zero angle measurement.

The purpose of the polynomial fit is to determine any time dependentdrift in the measurements made by the plurality of sensors. The cause ofthe drift may be temperature variation, though the cause of the drift isnot important. This particular step merely identifies the drift if itexists. The order of the polynomial is less than or equal to the numberof points to which the polynomial is being fit. In an alternateembodiment of the invention, the sinusoidal fit and the driftcompensation may be made simultaneously. A method of determining thecorrecting for the drift is discussed below with reference to FIGS.8-11.

Having determined this drift as a function of time, it is then removedfrom all the measurements made. This is indicated by 513 in FIG. 5B.Next, all the readings are corrected using laboratory determined modelparameters 515. This is discussed below with reference to FIG. 6.

Still referring to FIG. 5B, accelerometer based angular values areobtained for the static survey 517. This includes a determination ofhigh side tool face angle (HSTF), the inclination, and total gravityfield (TGF). Next, a sinusoid is fit to the measurements 519 using thecorrected HSTF. The variables for the fit are the bias, Scale Factor,and phase. Gyro based angular values for the static survey aredetermined 521. Bias values are calculated from sinusoidal fitting ofthe gyro measurements 523. This is done separately for the x- andy-gyros. Next, the x- and y-rates are calculated at 527 in FIG. 5C. Thisis the end of the static survey 529.

Turning now to FIG. 6, there is a further discussion of details of 515in FIG. 5B. The operations involved include an application of a scalefactor correction for the temperature at the final position 601. A biascorrection as obtained from the last survey is applied 603. Misalignmentcorrections are applied 605 and gravity dependent bias corrections areapplied to R_(x) and R_(y).

Some details of the “steering” mode are next discussed with reference toFIG. 7. Sample readings are taken at a high rate, typically about 15 Hz701. A moving average for the accelerometer raw readings is kept,typically over a one second time interval 703. A new value of the R_(z)is determined for each sample 705. These are done separately from the x-and y-gyros and the two values are averaged.

Still referring to FIG. 7, the R_(z) values are integrated with respectto time to find the change in the gyro toolface angle GTF 707. Thevalues derived for Rx, Ry, and Rz by any method when the tool is at restshould read components of the earth's rotational field which alwayscombine to produce the amplitude of the earth's known constant rotationrate of 15.04 degrees per hour. As a quality check, and to optimizeresults, the solutions can be iterated for the calibration terms and themultiple positions such that an optimal fit results in the minimumdeviation from the ideal earth field values. This combined looping anditeration through the multiple positions and adjusting the calibrationparameters to produce the optimum residual error in the earth field(gravity, magnetic, and/or rotational) follows the techniques disclosedin the SPE paper # 19546, by Estes & Walters, in 1989, and is commonlycalled “Total Field Calibration.” This change in the gyro toolface angle(from the running integral) is added to original starting toolface 707to give the current gyro toolface angle. A moving average for angularvalues is kept (typically over a 10 second interval) 709. This is the“Steering Gyro TF” value that may be telemetered uphole for enablingsteering decisions to be made. This is continued until timeout periodhas elapsed (˜30 minutes) 711, defining the end of the steering mode.

Turning now to FIG. 8, a method of correcting for temperature drift isdiscussed. Although all significant error terms are corrected byapplication of a lab-derived thermal model prior to the fitting of asinusoid for computation of angular values, this model correctionprocess is not complete. There are still residual errors that distortthe ideal sinusoidal shape of the rate measurements vs the indexedpositions. This is largely due to the practice of acquiring labcalibration data after thermal stabilization has occurred, whiledownhole operation at a survey station often occurs during thermallyunstable conditions. It is desirable to save battery power, thus thesurvey station operation is often initiated after a period during whichthe gyro is turned off, and is now increasing in temperature. Usually,during rapid temperature rise, the gyro exhibits errors which are afunction of temperature, although the temperature sensor has not yetreached the corresponding amplitude.

This method assumes that the measured gyro output signal, after applyingthe temperature correction factors, is a composite of a sine wave fromthe actual earth rate felt on the sensitive axis during indexing and aresidual bias shift that responds linearly with temperature. Theresponse is assumed to be near linear due to the small magnitude oftemperature change over the indexing time period. These residualtemperature-dependent errors are assumed to be primarily bias errors,since the majority of the other temperature-dependent errors have beencompensated already by the thermal model coefficients. The gyroscope isknown to have very large bias errors, which dominate the other errors.It is reasonable to assume that the errors left over are bias errors,and over a short temperature excursion that they are a linear functionof temperature. A source of error is the fact that the gyro has a muchsmaller time constant than the temperature sensor, so that the gyro isresponding to a temperature that is different from that indicated by thetemperature sensor. Unlike all other temperature correction factors,scale factor and mass balances terms, for example, this temperaturedependent bias is problematic to determine in laboratory calibrationsover such a small temperature span and also reasonably straightforwardto correct during the survey station computation.

FIG. 8 shows the ‘true rate’ signal 801 that represents the idealsinusoid which will always be the characteristic of the resulting rateapplied to the gyro when the sensor housing is indexed. This is true inall cases when the gyro sensitive axis is not null to the earth rate.Additionally, it shows the ‘temp drift’, the temperature change 803 overthe time required to position the housing. Due to the linearrelationship of temperature change and bias shift, the characteristicsof the ‘temp drift’ waveform are shared by the bias shift as well.Finally, ‘total rate’ (measured rate) is the composite 805 of the truesine gyro signal and the gyro bias shift as a result of temperaturechange.

After acquiring the signal and applying the laboratory determinedtemperature correction factors, it is the ‘total signal’ that isactually measured. The present invention uses an iterative process thatwill progressively break apart the two components to extract the truesine portion of the signal. FIG. 9 shows the measured ‘rate’ signal 821and a sine wave 823 fitted to it using motor position as the x-axis. Thefit error 825 is calculated and passed onto the next portion of themethod. FIG. 10 shows the same sine fit error 825 now plotted using thenominal temperature change measured by the temperature sensor as thex-axis. This error is now fitted with a linear fit 843, usingtemperature change as the x-axis. This linear fit of the sine fit erroris an approximation of the residual bias shift due to temperature changein the original signal and will be subtracted from the original signalduring the next iteration of the method. The process is repeated ifnecessary, and the final result is shown in FIG. 11 with the correctedgyro readings 851 as a function of angular position and the bias 853.

The bias correction has been described above with reference togyroscopic measurements. The bias correction method is equallyapplicable to other types of survey measurements, such as those made byaccelerometers, that are also affected by bias and a temperaturedependent bias. A downhole processor then controls the drillingdirection based on the corrected gyroscope and accelerometermeasurements.

Steering a drilling assembly during drilling operations often results inwild angular toolface swings as the bit slips and grabs the stratifiedrock formations. This results in turn rates on the z-axis with widedynamic range. In typical operations, a misalignment of less than 1milliradian results in the x- or y-axis signal being too small fordetection of normal rates of rotation about the z-axis. An upper boundon the misalignment is set by the fact that with values greater than 100milliradians, the x- or y-output signals may exceed the operating rangeof the A/D converter. A preferred range for use of the method of theinvention is between 5 and 20 milliradians.

The invention has been described above with reference to surveyingoperations and drill-steering applications. The methodology describedabove may also be used for wireline applications, or for slicklinesurvey instruments. For wireline applications, the survey mode could beentered at any desired time rather than being limited to time periodswhen drilling is suspended, since drilling operations are not involved.It can also be used in a memory-based “gyro drop shot” configuration.

While the foregoing disclosure is directed to the preferred embodimentsof the invention, various modifications will be apparent to thoseskilled in the art. It is intended that all variations within the scopeand spirit of the appended claims be embraced by the foregoingdisclosure.

1. A method of using a two-axis gyroscope on a housing for determining arate of rotation of said housing about a third axis, said two axes ofthe two-axis gyroscope being substantially orthogonal to each other,wherein said third axis has a small deviation from orthogonalityrelative to at least one of said two axes.
 2. The method of claim 1further comprising: (a) measuring an output of said two-axis gyroscopealong said at least one of said two axes in response to said rotationabout said third axis; and (b) determining from said output and amisalignment term an estimate of said rate of rotation about said thirdaxis.
 3. The method of claim 1 wherein said at least one of said twoaxes comprises both of said two axes, the method further comprisingdetermining said rate of rotation by averaging measurements made by twocomponents of said two-axis gyroscope in response to said rotation. 4.The method of claim 2 further comprising using a relation of the form:$R_{x} = {\frac{S_{x}}{F_{x}} - B_{x} - B_{xg} - {M_{x}R_{z}}}$ whereR_(x) is a rotation rate about said at least one axis, S_(x) is anoutput of said gyroscope corresponding to said at least one axis, F_(x)is a calibration scale factor for said at least one axis, B_(x) is abias for the at least one axis, B_(xg) is a bias term for said at leastone axis that is gravity related, M_(x) is said misalignment term.5.-26. (canceled)
 27. A method of compensating measurements made by adownhole survey instrument, the method comprising: (a) makingmeasurements with the downhole survey instrument at a plurality ofrotational positions; (b) applying a first correction to saidmeasurements using a thermal model to give a first set of correctedmeasurements; (c) fitting a sinusoidal function of angular position tothe first set of corrected measurements; (d) fitting a polynomialfunction of temperature to a residual remaining after said sinusoidalfitting; and (e) determining a corrected bias for said measurements madeby the downhole gyroscope using results of said polynomial fitting. 28.The method of claim 27 wherein said survey instrument comprises agyroscope.
 29. The method of claim 27 wherein said survey instrumentcomprises an accelerometer.
 30. A system for making downhole surveymeasurements, the system comprising: (a) a downhole survey instrumentwhich makes survey measurements at a plurality of rotational positions,and (b) a processor which: (i) applies a first correction to saidmeasurements using a laboratory-derived thermal model to give a firstset of corrected measurements, (ii) fits a sinusoidal function ofangular position to the first set of corrected measurements, (iii) fitsa polynomial function of temperature to a residual remaining after saidsinusoidal fitting; and (iv) determines a corrected bias for saidmeasurements made by the downhole gyroscope using results of saidpolynomial fitting.
 31. The system of claim 30 wherein said surveyinstrument comprises a gyroscope.
 32. The system of claim 30 whereinsaid survey instrument comprises an accelerometer.
 33. The system ofclaim 30 wherein said survey instrument is conveyed downhole on one of(A) a wireline, and, (B) a drilling tubular.